# The Pelayo Family Plays Roulette: The Prequel

1 Pages Posted: 2 Jun 2017

See all articles by Phillip E. Pfeifer

## Phillip E. Pfeifer

University of Virginia - Darden School of Business

## Samuel E. Bodily

University of Virginia - Darden School of Business

## Manel Baucells

University of Virginia - Darden School of Business

### Abstract

The case presents data from 70,340 spins of four roulette wheels: three of which are real ("imperfect") and one of which is simulated ("perfect"). The challenge posed is to identify which of the four is the simulated wheel. After weeks spent recording spin results at their local casino, the members of the Pelayo family think they have identified three imperfect wheels. Before they start betting, they want to be certain that the three wheels they identified as imperfect are easily distinguishable from a theoretically perfect wheel.This case has been used successfully in Darden's MBA elective about data analysis. That course introduced pivot tables and the chi-squared goodness-of-fit test using the case “The Roulette Wheel” (UVA-QA-0718). Discussion of the “The Pelayo Family Plays Roulette” probably will not require an entire class period. One option would be to hand out this case during the discussion of “The Roulette Wheel” as something of a follow-on.

Excerpt

UVA-QA-0847

Jun. 20, 2016

The Pelayo Family Plays Roulette: The Prequel

Dear Student,

For six weeks, my extended family (six people total) spent five to six hours a night at the Casino Gran Madrid (Figure 1) recording the outcomes of thousands of spins of roulette wheels. Each morning, I entered these data into my personal computer.

I believe there is no such thing as a perfect wheel (Figure 2), and that it takes lots of observations to find the small imperfections that must exist in every wheel. We believe we have found three wheels with imperfections large enough to be discovered, and I would like to ask you to use your data analysis skills to help make sure.

. . .

Keywords: data analysis, statistics, goodness-of-fit test, chi-squared, probability, roulette wheel

Suggested Citation

Pfeifer, Phillip E. and Bodily, Samuel E. and Baucells, Manel, The Pelayo Family Plays Roulette: The Prequel. Darden Case No. UVA-QA-0847. Available at SSRN: https://ssrn.com/abstract=2975188